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An efficient technique based on higher order Haar wavelet method for Lane–Emden equations

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  • Swati,
  • Singh, Mandeep
  • Singh, Karanjeet

Abstract

This paper aims at introducing an effective computational technique for finding the solution to well-known Lane–Emden type equations by employing the higher order numerical method based on Haar wavelet expansions. A modified version of Haar wavelet method, known as Higher order Haar wavelet method has been discussed to enhance the accuracy and rate of convergence. This numerical method successfully tackles the singularity at x=0 and gives the approximated solution of the given Lane–Emden type equations in terms of higher order Haar wavelet expansions. Various numerical examples of Lane–Emden type equations have been discussed to demonstrate the validity and efficiency of the proposed algorithm. The numerical findings obtained by employing the present method have been presented with the aid of tables and graphs. Also, the comparisons made with well-known existing techniques, including finite difference schemes, various spline and decomposition methods, help to manifest the better accuracy and high efficiency of the present approach.

Suggested Citation

  • Swati, & Singh, Mandeep & Singh, Karanjeet, 2023. "An efficient technique based on higher order Haar wavelet method for Lane–Emden equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 21-39.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:21-39
    DOI: 10.1016/j.matcom.2022.10.031
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    References listed on IDEAS

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    1. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    2. Roul, Pradip & Prasad Goura, V.M.K., 2019. "B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 428-450.
    3. Bulut, Fatih & Oruç, Ömer & Esen, Alaattin, 2022. "Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 277-290.
    4. Goura, V.M.K. Prasad & Roul, Pradip, 2019. "Erratum to: B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 198-201.
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    Cited by:

    1. Arsen Palestini & Simone Recchi, 2024. "Qualitative Properties of the Solutions to the Lane–Emden Equation in the Cylindrical Setup," Mathematics, MDPI, vol. 12(4), pages 1-11, February.

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